Again, the deciding principle is that inertial clocks don’t slow down—only non-inertial ones do. Clock B is moving inertially; if an observer moving with the falling clock dropped a ball, it would not fall faster than he does, but would continue to float alongside him. Clock A is not moving inertially, according to general relativity, since the force of gravity can be equated with a non-inertial frame of reference. Therefore it’s clock B that runs at the normal rate, and clock A that runs slow. That is precisely the prediction that general relativity makes: Clocks lower down in a gravitational field run slower than clocks higher up.
Here’s another way to put it. Suppose you’re in a big elevator shaft, 1 km tall, in empty space, free from the effects of gravity. There’s a clock at the top of the shaft—that’s clock B—and a clock in the elevator car at the bottom—that’s clock A. As long as the elevator doesn’t move, both clocks are in the same reference frame and run at the same rate.
If the elevator begins accelerating upward at 1 g, it goes faster and faster until it hits the top of the shaft and we can finally compare the clocks. Both clocks think they’re running at a uniform rate, but because clock A is accelerating, it must be running slower than clock B. How much slower? If you accelerate at 1 g, then when you’ve gone 1 km, you’re moving at approximately 140 m/s (about 310 mph). Special relativity says that a clock moving 140 m/s runs slow by about 1 part in 9 trillion.
By Einstein’s principle of equivalence, there is no difference between this situation and the original one, so a clock on the ground runs about 0.00000000001% slower than one that’s 1 km up in the air. Specialized atomic clocks can verify this prediction to better than one part in 1,000.
However, the same reasoning allows us to compare clocks at any height. Suppose clock A remains on the ground, but clock B is raised to an enormous height—an infinite height, in fact. Let’s run the same experiment, letting B free-fall in its inertial frame down to the ground. How fast is it moving when it hits the ground? The speed depends only on the mass of the Earth and its radius:
(14) v = sqrt(2GM / r)
Einstein’s general relativity simply says that you plug that speed into the special relativity equations, and that tells you how slow clocks run at that height. If we perform the necessary substitutions, we get a time dilation effect of
(15) t/to = sqrt(1—(2GM / rc2))
This means that clocks on the surface of the Earth run slow by about 1 part in 1.4 billion. Now that is large enough to be verified experimentally—in fact, GPS devices, which depend on clocks aboard geostationary satellites in orbit far above the Earth, must take into account the relative speed-up of those clocks compared with those on Earth.
Incidentally, the same equivalence principle allows us to deduce that lengths are compressed in a gravitational field, just as they are in objects moving at a high speed. For example, if you take a perfectly rigid sphere (one that isn’t deformed by tidal forces) from outer space and bring it back to the earth, its height is actually less than its width. Unfortunately, even if there were such a thing as a perfectly rigid sphere, you couldn’t measure this change, because when you measure the width with a ruler, you’re holding the ruler horizontally and it’s uncompressed, whereas when you’re measuring the height, you’re holding the ruler vertically and it’s compressed just as much as the object! So the measurements will come out just the same. As far as I know, there are no good experiments to test this particular prediction of relativity.
Adapted from Astronomical Games: May 2001.
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Brian Tung is a computer scientist by day and avid amateur astronomer by night. He is an active member of the Los Angeles Astronomical Society and runs his own astronomy Web site. His previous publications in Strange Horizons can be found in our archives.
Reason, Sexuality, and the Self in Libertarian Science Fiction Novels
By Greg Beatty
9/17/01
Defining the Genre
Trying to define science fiction is always a good way to start a controversy. Allegiances emerge quickly, and it’s virtually certain that people will start talking past one another almost as soon as they start talking. Add a qualifier, such as “libertarian,” and the task gets harder. For the purposes of this essay, I’ll try to keep my discussion focused by using a fairly basic definition of the genre assembled from a number of sources. In his study of the fantastic, Tzvetan Todorov suggests that there are two kinds of literary genres: theoretical genres and historical genres. Theoretical genres are defined by the presence of specific key structures, which may exist in only a single example. I follow Darko Suvin, and argue that science fiction is defined by the presence of a “novum,” some new thing that works as a rupture in the assumed fabric of reality and demands a new form of narrative that coherently integrates this novum. This novum can fall into almost any category—Suvin suggests biology, social structure, physical reality, and so on. What I want to ask is, what sort of “new things” does libertarian science fiction posit, and what do they mean?
For Todorov, a historical genre is produced through an accrual of genre conventions and narrative tropes shaped by an ongoing interaction among a community of readers. It’s this sort of thing that makes it possible to legitimately say, “I can’t define science fiction (or pornography, or westerns), but I know it when I see it!” and have the claim make sense. To help answer my core questions, I want to document the genre conventions that libertarian science fiction shares—the things that accompany their novums, and which slip by unnoticed in the authors’ rush to explore freedom. I do this, because like John Cawelti, I assume that these genre conventions indicate what a specific readership finds socially acceptable or desirable. These genre conventions are also where we’ll find the ideological underpinnings of these books. If we look at the definition of freedom that libertarian science fiction uses, we’ll find a striking pattern of assumptions about the nature of reason, sexuality, and the self.
Libertarian Science Fiction
Since libertarian science fiction is also a debatable term, I’m only looking at the novels that have won the Prometheus Award, the award given annually since 1982 by the Libertarian Futurist Society. The award was founded in 1979 by L. Neil Smith to honor libertarian science fiction, and was given that year to F. Paul Wilson for Wheels Within Wheels, but due to the cost of the award—then a gold coin valued at $2500—and the lack of a formal supporting organization, the award fell into limbo until adopted by the LFS. The public documents of the Society itself provide our first clues as to the nature of these books; it was founded in 1982 “to provide encouragement to science fiction writers whose books examine the meaning of freedom.” This claim, so open-minded as to be philosophical rather than political in nature, is immediately qualified. The Prometheus Award is given to the “best libertarian novel of the year.” The best “examinations of freedom”—a term which could include challenges to it, rejections of it, or positing proper limits for it—will be found specifically in libertarian science fiction. The selections standards are therefore narrowly pre-defined: examining freedom will always produce works in favor of it, and these works will all be libertarian.
Prometheus
Defining libertarianism can be as difficult as defining science fiction, even for someone who has been in and out of the libertarian movement for decades, such as myself. Clues to the complexity of this struggle can be found in the name of the award, and in what the Society says it represents. In Greek mythology the god Prometheus, whose name means “forethought,” was charged by Zeus to create mankind. However, Prometheus’s brother, Epimetheus (“afterthought”) got the job of creating the animals, and followed his first impulses by giving out the best gifts lavishly. The eagle got flight, the tiger claws, and so on, until there was nothing left for humanity when Prometheus got there. He thought it through, and formed mankind in the image of the gods. He then stole fire, symbolic of reason, from the heavens, and gave it to man. Zeus, who had decreed that fire was to remain the property of the gods, was so angry at this that he chained Prometheus to a rock, with a vulture continually eating his liver. However, Prometheus was also tortured because he knew the identity of Zeus’s offspring who would someday overthrow him. Prometheus refused to tell the name, and suffered for years before being freed by Hercules. Therefore, in addition to being responsible for the uplift of mankind, Prometheus was instrumental in overthrowing divine tyranny. The Prometheus award, however, stands for “free trade and free minds,” reducing free mental activity to that of economic man in the marketplace, and equating free trade (whatever its motives) with freedom, and with rebellion against moral tyranny, conveniently ignoring the offense against property rights committed by Prometheus.